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June 16th, 2010, 05:57 PM  #1 
Joined: Feb 2009 Posts: 76 Thanks: 0  The range of a matrix transformation
How to do you determine if a vector (w) is in the range a matrix transformation. Let f: R^2 > R^3 f(x) = Ax Vector w Why is it a no? My work: ( I don't know if I'm doing it right) and why is for Vector w, it's a yes? The book says that the set of all images of the vectors in R^n is called the range of f. I don't know what it means. Can someone please explain to me how to determine the range. Thanks in advance 
June 16th, 2010, 07:21 PM  #2 
Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 1  Re: The range of a matrix transformation
You want w= f(v) = Av, where v is a vector . The equation should be: You cannot substitute values of w into v, you need to see if any value of v, when multiplied by A gives you w. See if there is any v=[x,y] which satisfies this equation. Edit: Some clarification. "The set of all images" is the set . So, if w is in the image, w=f(v) for some vector v in R^2. To check if such a vector exists, see if there is any vector which satisfies f(v)=w. 

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